A new method of deconvolution is described which uses prior knowledge about the solution to derive some of the information obscured in the data because of the smoothing nature of convolution and the presence of noise. It uses a regularized least-squares criterion of agreement with the data, according to which the computed solution will lead to a minimum variance of noise and also be smooth in the sense of minimum variance of its second-differences. In addition, the present optimum deconvolution method also constrains this solution to satisfy prior knowledge about it by using a combination of a new algorithm for incorporating bounds on the solution like positivity, and the Lagrange multiplier method for equality-constraints.